Question

use the given triangles to evaluate the following expression. if necessary, express the value without a square root in the denominator by rationalizing the denominator.
\\(\cos \left( \dfrac{\pi}{6} \
ight)\\)
\\(\cos \left( \dfrac{\pi}{6} \
ight) = \square\\)
(simplify your answer. type an exact answer, using radicals as needed. use integers or fractions for any numbers in the expression. rationalize all denominators.)

Explanation:

Step1: Convert radians to degrees

$\frac{\pi}{6} \text{ radians} = 30^\circ$

Step2: Recall cosine definition for right triangles

$\cos(\theta) = \frac{\text{adjacent side}}{\text{hypotenuse}}$

Step3: Identify sides for 30° angle

For $30^\circ$, adjacent side = $\sqrt{3}$, hypotenuse = 2

Step4: Calculate the cosine value

$\cos(30^\circ) = \frac{\sqrt{3}}{2}$

Answer:

$\frac{\sqrt{3}}{2}$